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Short answer: "This needs to be fixed" is correct. Don't use "This needs fixed."

Longer, more interesting answer: Ordinarily, you must use to be with a past participle such as fixed. However, in certain parts of the United States there is a peculiar regional practice of omitting to be when using needs or wants with a past participle, and in those areas, "this needs fixed" is exactly the kind of sentence you would expect to hear. You would never want to use this construction for general consumption, however.